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An Electronic Travel Authorization (eTA) is a new requirement for foreign nationals from visa-exempt countries arriving in Canada by air, whether to visit the country directly or to pass through in transit.

A strengthening U.S. economy has spurred the largest pickup in immigration since before the recession, driven by Asian newcomers and a gain in Hispanic arrivals.

The number of foreign-born people in the U.S. grew by 523,400 last year, according to the Census Bureau. That beat the previous year’s net gain of roughly 446,800 and is the biggest official jump since 2006. The numbers don’t distinguish between authorized and unauthorized immigrants.

Asian immigrants, including Chinese students and highly skilled workers from India, fueled many of the gains.

Demand among U.S. employers for visas for skilled foreign workers—the so-called H-1B visas dominated by Indian workers—has rebounded. Businesses reached the federal cap on applications in less than a week this year; in 2012, it took three months, and in 2011, eight months, to fill all the slots.

Meanwhile, Hispanic immigration is picking up, after slowing to a trickle in recent years as weak job and home-construction markets prompted many workers—often less-educated and in the U.S. illegally—to return home.

Approximately 27% of last year’s new immigrants were Hispanic, compared with about 10% in 2012 and less than 1% in 2011, census figures show. More Mexicans came to the U.S. last year than left—a notable shift after several years in which the opposite happened.

With construction work perking up, Texas has seen a rise in Hispanic immigrants, said Cristina Tzintzún, executive director of the Workers Defense Project, a Austin group that trains and advocates for low-wage workers.

Annual growth in the U.S. foreign-born population remains lower than the 800,000 or so average of a decade ago. Tighter borders, along with declining fertility and increased economic opportunities in Mexico, make it unlikely Hispanic immigration will surge the way it did in the 1990s—leaving Asians the dominant force.

But the census data show that six years after the recession began, America is restoring its reputation as an economic beacon among immigrants, even as other nations, including in Asia, become more attractive. If demand for high-skilled workers grows and Hispanic immigration revives, that could also mean U.S. businesses are feeling more bullish about the economy’s prospects.

America’s Mexico-born population marks the biggest wave of immigration from a single country in U.S. history, but the recession helped bring that to a halt. Now there are signs of a shift: The Mexico-born population grew by nearly 22,000 last year, on net, after shrinking about 109,000 in 2012 as more Mexicans left the U.S. than came, Mr. Frey said.

Another sign of the stronger U.S. economy: Money sent by Mexicans abroad to individuals back home has bounced back. More than $2 billion in such remittances flowed into Mexico in August, the vast majority from the U.S., up from $1.9 billion a year earlier and $1.3 billion in January 2010, figures from Mexico’s central bank show.

Pew estimates there were 11.3 million unauthorized immigrants living in the U.S. as of March 2013, compared to 11.2 million in 2012, an increase that isn’t statistically significant.